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Influence functions, followers and command games

Author

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  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Agnieszka Rusinowska

    (GATE - Groupe d'analyse et de théorie économique - UL2 - Université Lumière - Lyon 2 - ENS LSH - Ecole Normale Supérieure Lettres et Sciences Humaines - CNRS - Centre National de la Recherche Scientifique)

Abstract

We study and compare two frameworks: a model of influence, and command games. In the influence model, in which players are to make a certain acceptance/rejection decision, due to influence of other players, the decision of a player may be different from his inclination. We study a relation between two central concepts of this model: influence function, and follower function. We deliver sufficient and necessary conditions for a function to be a follower function, and we describe the structure of the set of all influence functions that lead to a given follower function. In the command structure introduced by Hu and Shapley, for each player a simple game called the command game is built. One of the central concepts of this model is the concept of command function. We deliver sufficient and necessary conditions for a function to be a command function,and describe the minimal sets generating a normal command game. We also study the relation between command games and influence functions. A sufficient and necessary condition for the equivalence between an influence function and a normal command game is delivered.

Suggested Citation

  • Michel Grabisch & Agnieszka Rusinowska, 2008. "Influence functions, followers and command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00355632, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00355632
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00355632
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    References listed on IDEAS

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    Cited by:

    1. Emmanuel Maruani & Michel Grabisch & Agnieszka Rusinowska, 2011. "A study of the dynamic of influence through differential equations," Documents de travail du Centre d'Economie de la Sorbonne 11022, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Förster, Manuel & Grabisch, Michel & Rusinowska, Agnieszka, 2013. "Anonymous social influence," Games and Economic Behavior, Elsevier, vol. 82(C), pages 621-635.
    3. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence with an ordered set of possible actions," Theory and Decision, Springer, vol. 69(4), pages 635-656, October.
    4. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
    5. Ulrich Faigle & Michel Grabisch, 2017. "Game Theoretic Interaction and Decision: A Quantum Analysis," Games, MDPI, vol. 8(4), pages 1-25, November.
    6. Buechel, Berno & Hellmann, Tim & Klößner, Stefan, 2015. "Opinion dynamics and wisdom under conformity," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 240-257.
    7. Michel Grabisch & Agnieszka Rusinowska, 2010. "Different Approaches to Influence Based on Social Networks and Simple Games," Post-Print hal-00514850, HAL.
    8. Karos, Dominik & Peters, Hans, 2015. "Indirect control and power in mutual control structures," Games and Economic Behavior, Elsevier, vol. 92(C), pages 150-165.
    9. Agnieszka Rusinowska & Rudolf Berghammer & Harrie de Swart & Michel Grabisch, 2011. "Social networks: Prestige, centrality, and influence (Invited paper)," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633859, HAL.
    10. Tomas Rodriguez Barraquer, 2013. "From sets of equilibria to structures of interaction underlying binary games of strategic complements," Discussion Paper Series dp655, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    11. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, vol. 2(1), pages 1-33, March.
    12. Dominik Karos, 2016. "Coordinated Adoption of Social Innovations," Economics Series Working Papers 797, University of Oxford, Department of Economics.

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    More about this item

    Keywords

    influence function; follower function; lower and upper inverses; kernel; command game; command function; minimal sets generating a command game;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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